Frege's Contribution to Philosophy of Language

Gottlob Frege’s contributions to philosophy of language are so numerous and so fundamental that it is difficult to imagine the field without them. That this should be so was not, however, Frege’s original intent. Frege was trained as a mathematician, and most of his non-foundational mathematical work lay at the intersection of geometry and complex analysis. That makes it at least somewhat surprising that he should have made any contribution to the study of language, let alone one so profound. But mathematics, in Frege’s time, was itself in a state of upheaval, many of its most basic notions being subjected to a thorough re-examination. Among the central issues in Frege’s intellectual environment was how we should understand the relation between geometry and arithmetic, the latter understood in a broad sense, as including the theory of all numbers, natural, real, and complex.1 Though by no means universal, it was a common view that geometry was the more fundamental of the disciplines. In part, this view derived from Kant, who had famously argued that even our knowledge of basic number theory is founded upon pure a priori intuition of roughly the same sort that he claimed underlay our knowledge of the axioms of Euclidean geometry. The view had other sources, too. For example, it was as common then as it is now to think of the complex numbers as points (or perhaps vectors) in the Euclidean plane. Such a treatment of the complex numbers would suggest, again, that geometrical knowledge is more basic than arithmetical knowledge. Frege, like many mathematicians of his time, rejected this Kantian view. His strategy for refuting Kant was to demonstrate that “. . . arithmetic is a branch of logic and need not borrow any ground of proof whatever from either experience or intuition” (Gg, §0) by identifying a small set of recognizably logical principles,